6 papers
Central limit theorems for high dimensional lattice polytopes: cosmological polytopes
Torben Donzelmann, Martina Juhnke, Benedikt Rednoà +1
We study cosmological polytopes induced by ErdÅs--Rényi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice pol…
Central limit theorems for high dimensional lattice polytopes: symmetric edge polytopes
Torben Donzelmann, Martina Juhnke, Benedikt Rednoà +1
We investigate symmetric edge polytopes generated by ErdÅs--Rényi random graphs in a high-dimensional regime. These objects provide a natural and largely unexplored model of rand…
On cosmological polytopes, their canonical forms and their duals
Anna Birkemeyer, Torben Donzelmann, Mieke Fink +1
We compute the canonical form of the cosmological polytope for any graph in terms of the dual of the shifted cosmological polytope in two different ways. On the way, we provide an…
Symmetric (co)homology polytopes
Torben Donzelmann, Thiago Holleben, Martina Juhnke
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to a…
Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices
Jhon B. Caicedo, Martina Juhnke, Germain Poullot
Counting lattice points and triangulating polytopes is a prominent subject in discrete geometry, yet proving Ehrhart positivity or existence of unimodular triangulations remain of…
Unimodality of the number of paths per length on polytopes: Examples, counterexamples, and a central limit theorem
Martina Juhnke, Germain Poullot
Because of its importance in combinatorics and optimization we study the full distribution of the lengths of monotone paths of a convex polytope. De Loera had conjectured that the…